Gauss, Ramanujan and Hypergeometric series

This year is the bicentennial of the discovery of the second order Ordinary Differenential Equation
by Carl Friedrich Gauss. While Gauss noted 4 solutions and 15 recurrence relations for the contiguous
hypergeometric functions, it was Kummer who discovered that there are 24 solutions to this equation in
the year 1814. In recent times, it has been shown that these 24 solutions can be related to the
24 symmetries of the cube. Besides presenting this result of the author and his collaborators, an i
ntroduction will be given to the generalized hypergeometric series and their intimate relation to the
angular momentum coupling and recoupling coefficients in the Quatum Theory of Angular Momentum.